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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="OrderSubfield"></a>
OrderSubfield
</h2>

Returns all non-trivial subfields of given degree <tt> m</tt>.
If no <tt> m</tt> is
specified,
all subfields are calculated.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := OrderSubfield(o);
L := OrderSubfield(o, m);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>list of suborders</td>
</tr>
<tr>
<td>order</td>
<td><pre>  O  </pre></td>
<td>the given order</td>
</tr>
<tr>
<td>small integer</td>
<td><pre>  m  </pre></td>
<td>the prescribed degree of subfields</td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#OrderSubfieldSub">OrderSubfieldSub</a>

<p>

<h3>
Description:
</h3>
This function calculates all non-trivial subfields of
given degree <tt> m</tt>.
If no <tt> m</tt> is specified, all non-trivial subfields are calculated.
The result is a list <tt> L</tt>, which contains the calculated subfields
as orders. The function uses the algorithms described in
Kl1,KlPo1,Kl2\par
It is possible that this function returns the same order
for two subfields. In this case, these subfields are isomorphic,
but not identical. In the example below, the three subfields are
isomorphic
If the running time for this function seems too long, the user
may want to try OrderSubfieldSub.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Computation of subfields of given degree. 
<pre>

kash> O:=Order(Poly(Zx,[1,-3,5,-5,5,-3,1]));
Generating polynomial: x^6 - 3*x^5 + 5*x^4 - 5*x^3 + 5*x^2 - 3*x + 1

kash> L:=OrderSubfield(O,3);
[ Generating polynomial: x^2 + 23
    , Generating polynomial: x^3 - 3*x^2 + 2*x - 1
    , Generating polynomial: x^3 - 2*x^2 + 3*x - 1
    , Generating polynomial: x^3 - 3*x^2 + 2*x - 1
     ]
kash> elt:=Elt(L[2],[1,1,1]);
[1, 1, 1]
kash> EltMove(elt,O);
> [2, -3, 3, -5, 3, -2]

</pre>

<p>


<hr>

<p>
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